Alpha Power Poisson-G Distribution With an Application to Bur XII Distribution Lifetime Data
Bibliographic record
Abstract
We propose a new method of adding two shape parameters to a family of distributions for more flexibility and wider scope of applications called Alpha power Poisson-g distribution. A special case has been considered in details namely; one parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, moment generating function, mean and median deviation, Bonferroni and Lorenz curve, order statistics and expression of the Renyi entropies are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Further we consider an extension of the two-parameter Bur XII distribution also, mainly for data analysis purposes. Three data sets have been analyzed to show how the proposed models work in practice. We also carried out Monte Carlo simulation to further investigate the properties of the proposed method of estimation.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".